See this is where you are generalizing your experiences of women to be ALL women. She isn't like that at all, I believe she genuinely does care about me still and wants the best for me but as you all say, her saying this only serves to make her feel better about herself, it doesn't really help me in the slightest.
And in regards to telling her I'm going on dates, again, that isn't going to achieve anything and its none of her business really anyway. She's thought long and hard about her decision to end our relationship, I believe she has made her decision and will stick by it, she won't come "grovelling" back if she finds out i'm seeing other people - nor would I want her to. Its over, I've accepted it and I'm getting on with moving on, as is she.
She will find out sooner or later through the grapevine that I'm on Tinder and have been on dates as I've already swiped past mutual friends and you know what women are like, they love to tell people who they've seen on Tinder and such like! Wouldn't surprise me if she already knew I was using data apps but as she is in no position to have any say or question it, she hasn't mentioned it, which is how it should be imo.